منابع مشابه
Relating Polynomial Time to Constant Depth
Going back to the seminal paper [FSS84] by Furst, Saxe, and Sipser, analogues between polynomial time classes and constant depth circuit classes have been considered in a number of papers. Oracles separating polynomial time classes have been obtained by diagonalization making essential use of lower bounds for circuit classes. In this note we show how separating oracles can be obtained uniformly...
متن کاملCounting Hierarchies: Polynomial Time and Constant Depth Circuits
In the spring of 1989, Seinosuke Toda of the University of Electro-Communications in Tokyo, Japan, proved that the polynomial hierarchy is contained in P PP To-89]. In this Structural Complexity Column, we will brieey review Toda's result, and explore how it relates to other topics of interest in computer science. In particular, we will introduce the reader to The Counting Hierarchy: a hierarch...
متن کاملDefinability by Constant-Depth Polynomial-Size Circuits
A function of boolean arguments is symmetric if its value depends solely on the number of l 's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constant-depth polynomial-size sequences of boolean circuits, and discuss the complete characterization. (We treat both uniform and non-uniform sequences of circuits.) Our r...
متن کاملOn Relating Time and Space to Size and Depth
Turing machine space complexity is related to circuit depth complexity. The relationship complements the known connection between Turing machine time and circuit size, thus enabling us to expose the related nature of some important open problems concerning Turing machine and circuit complexity. We are also able to show some connection between Turing machine complexity and arithmetic complexity.
متن کاملRelating the Bounded Arithmetic and Polynomial Time Hierarchies
The bounded arithmetic theory S 2 is nitely axiomatized if and only if the polynomial hierarchy provably collapses. If T i 2 equals S i+1 2 then T i 2 is equal to S 2 and proves that the polynomial time hierarchy collapses to p i+3 , and, in fact, to the Boolean hierarchy over p i+2 and to p i+1 =poly .
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00061-9